The word problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable. (Q408527)

The Magnus break-down procedure solves the word problem in an arbitrary one-relator group. The problem arises if it is true that the word problem in every given one-relator group is decidable in polynomial time. There are large general classes of one-relator groups where this is the case, but at present it is not known if this holds in general. Here it is shown that in the Baumslag group \(\langle a,b\mid b^{-1}a^{-1}bab^{-1}ab=a^2\rangle\) the word problem is decidable in polynomial time.